Non-Abelian defects in fracton phases of matter

Fracton phases of matter host fractionalized topological quasiparticles with restricted mobility. A wide variety of fracton models with Abelian excitations had been proposed and extensively studied while the candidates for non-Abelian fracton phases are less explored. In this paper, we investigate the effect of twisted defects in Abelian fracton models. The twisted defect is launched by introducing a branch cut line hosting anyon condensate. In particular, these twisted defects, which alter different types of quasiparticles, carry projective non-Abelian zero modes. En route, such defects can be engineered via strong on-site hybridization along a branch cut which provides wide tunability and flexibility in experiment platforms. The braiding of twisted defects with projective non-Abelian Berry phases renders an avenue toward fault-tolerant quantum computation.